The sum of the squares of three consecutive odd integers is 683. what are the integers?

1 Answer
Feb 22, 2018

The required odd integers are \ \ \ 13, \ \ \ 15\ \ \ and \ \ \ 17

Explanation:

Let the three odd numbers be x − 2 , x and x + 2 . As sum of their squares is 683 , we have:

(x-2)^2+x^2+(x+2)^2=683

x^2-4x+4+x^2+x^2+4x+4=683

Simplify:

3x^2+8=683

Solve for x to get:

x=15

So, our required odd integers are\ \ \ 13, \ \ \ 15\ \ \ and \ \ \ 17

That's it!